Hard evidence and mechanism design

Abstract

This paper addresses how hard evidence can be incorporated into mechanism-design analysis. Two classes of models are compared: (a) ones in which evidentiary decisions are accounted for explicitly, and (b) ones in which the players make abstract declarations of their types. Conditions are provided under which versions of these models are equivalent. The paper also addresses whether dynamic mechanisms are required for Nash implementation in settings with hard evidence. The paper shows that static mechanisms suffice in the setting of "evidentiary normality" and that, in a more general environment, one can restrict attention to a class of three-stage dynamic mechanisms.Many contractual and public-choice settings are analyzed using mechanism-design theory, which is a useful framework for studying the implications of informational asymmetries. The typical mechanism-design model comprises a set of states (representing the parties' information), a set of physical outcomes, and a specification of preferences over outcomes and states. The typical implementation exercise involves designing a game form, which induces a game to be played in each state. In essence, the game form specifies how the parties may send messages to each other and to an external enforcer, who will select the outcome on their behalf. The parties' rational behavior in each state implies an outcome function (the outcome as a function of the state).In its standard "public choice" form, the mechanism-design framework abstracts from institutional and technological constraints beyond those that the modeler can represent in the definition

Implementation with partial provability

“…6 The example represents a general phenomenon -in many situations, proving a negative proposition ("agent i cannot do x" or "agent i does not have y") is difficult or impossible. 7 We refer to the set { i,s |i ∈ I, s ∈ S } as the preference structure. We say that a preference structure has state independent preferences if the preference of each player over A is independent of s. That is, for every i ∈ I and s, s ∈ S, we have i,s = i,s .…”

“…5 Lipman and Seppi (1995) first identified this condition, calling it the full reports condition. Most papers refer to this assumption as normality following Bull and Watson (2007). While most of the literature assumes normality, see Lipman and Seppi (1995), Glazer and Rubinstein (2001, 2006, Bull and Watson (2007), and Kartik and Tercieux (2010) for models which relax the assumption.…”

“…Most papers refer to this assumption as normality following Bull and Watson (2007). While most of the literature assumes normality, see Lipman and Seppi (1995), Glazer and Rubinstein (2001, 2006, Bull and Watson (2007), and Kartik and Tercieux (2010) for models which relax the assumption. We thank Kartik and Tercieux for pointing out that a previous draft of this paper stated an unnecessarily strong version of this property.…”

“…6 The piano player example appears in Lipman and Seppi (1995) who attribute it to Mike Peters. 7 For example, Hurwicz, Maskin, and Postlewaite (1995) and Postlewaite and Wettstein (1989) assume that a player who has x units of a good can prove that he has at least y units for every y ≤ x by simply showing y units. However, the player cannot prove that he has exactly x units because he might be hiding some units.…”

Discounts for Qualified Buyers Only

“…Grossman (1981) and Milgrom (1981)) and mechanism design with partially verifiable information (e.g. Green and Laffont (1986) and Bull and Watson (2005)). In these literatures, all messages are costless.…”